Why do we female humans (and possibly other mammals) have all our eggs
present in our ovaries at birth? Are there not advantages in making
new ones (like sperm) when needed?

Peter Hurst, a reproductive biologist at the University of Otago's Department
of Anatomy, responded.

These questions are interesting and relate to all mammals studied so far.
The first question can be considered by understanding the life of the egg
in the human baby's developing ovary.

Eggs are formed in the ovaries after many cell multiplications of young germ
cells. This starts in early foetal life and their number increases rapidly
to over a million in each ovary. Paradoxically many of these die before
birth whilst the remainder begin the special cell division known as meiosis
but stop part way through meiosis to become a final bank of quiescent eggs.
Each egg is surrounded by a layer of cells called granulosa cells to form
small ovarian follicles.

From birth through to puberty small follicles begin to grow but their eggs
and granulosa cells die so when cycles and ovulation patterns begin,
the number of follicles has declined to around 200,000. After puberty
maturation of hormone production by the brain, pituitary gland and ovaries
leads to the rapid growth and ovulation of, usually, a single follicle
midway through each menstrual cycle and its egg will have been the only
one to restart the process of meiosis again. As regular cycles continue
many other follicles will also be stimulated to grow but as before, they
degenerate and do not ovulate. By menopause the number of follicles is
reduced to none or very few.

Is there a reason why no new germ cells are produced in adult life?
We are not sure why females don't manufacture eggs from scratch as needed.
For women the maximum reproductive potential begins in late adolescence
and ends in the mid 30's. From 35 onwards reproductive capacity to achieve
and support a pregnancy declines and this becomes rapid after the age of 40.
Thus there may be biological and health advantages of decreasing and
not replacing germ cells in adults by this stage in life.